Suppose R is a real-valued function on RI k with R(y) = o(|y|

p)

as |y| → 0, for some p > 0. If Yn is a sequence of random vectors satisfying

|Yn| = oP (1), then show R(Yn) = oP (|Yn|

p). Hint: Let g(y) = R(y)/|y|

p with g(0) = 0 so that g is continuous at 0; apply the Continuous Mapping Theorem.